I don't have a complete answer, but it does looks like there was a "First Lady" series of rings.
The most significant thing I found was
this
from an antique jewellery company in California.
There are a couple of references to "First Lady" items on e-bay, but
they have turned out to be cubic zirconia, rather than diamond
(
link).
Maybe an email to the first company could get you some more information. Their email is listed on the site.
Sorry I couldn't find anything specific.